Find the period range and amplitude of the cosine function y=-4 cos 8x
The general form of a cosine function is y = A cos(Bx + C) + D, where A is the amplitude, B determines the period, C is the horizontal shift, and D is the vertical shift.
In the given function, y = -4 cos 8x, the amplitude is 4 and the vertical shift is 0 (since there is no constant added).
To find the period, we use the formula: period = 2π/B. In this case, B = 8, so the period is:
period = 2π/8 = π/4
Therefore, the period range is π/4 and the amplitude is 4.
To find the period and amplitude of the cosine function y = -4 cos 8x, we need to understand the general form of a cosine function.
The general form of a cosine function is y = A cos (Bx + C), where A represents the amplitude, B represents the frequency or number of cycles in the given interval, and C represents any horizontal shift.
Comparing it with the given function y = -4 cos 8x, we can see that:
A = -4 (amplitude)
B = 8 (frequency)
The amplitude of the function is the absolute value of the coefficient A, so the amplitude is 4.
To find the period, we know that the period of a cosine function is given by 2π/B. In this case, B = 8, so the period is 2π/8 = π/4.
Hence, the period range is π/4, and the amplitude is 4.